1. Field
The present disclosure is directed to transmission lines, and in particular on an apparatus and method based on a two-dimensional transmission line.
2. Related Art
It is always difficult to generate broadband signals with more bandwidth and/or quasi-single tone signals at higher frequencies due to the frequency limitations of passives and active devices. For example, in an integrated circuit process, the maximum frequency of operation for transistor is often limited by fT and fmax of the transistors. In fact, fT and fmax are maximum theoretical limits when the transistors current and power gains drop to unity, respectively. The transistor is hardly useful at such frequencies and therefore, to perform any kind of meaningful operation, be it analog amplification or digital switching, the circuits can only operate with bandwidths and frequencies that are only a small fraction of these limits (i.e., f T and fmax).
However, it is highly desirable to be able to generate extremely broadband signals with reasonable power for many applications, including (but not limited to) ultra-wideband impulse radio, ultra-wideband RADAR, and timing generation. At same time efficient generation of large amounts of RF power at higher frequencies has been the Holy Grail of microwave and RF designers.
Recently, there has been growing interest in using silicon-based integrated circuits at high microwave and millimeter wave frequencies. The high level of integration offered by silicon enables numerous new topologies and architectures for low-cost reliable SoC applications at microwave and millimeter wave bands, such as broadband wireless access (e.g., WiMax), vehicular radars at 24 GHz and 77 GHz [20], short range communications at 24 GHz and 60 GHz, and ultra narrow pulse generation for UWB radar.
Power generation and amplification is one of the major challenges at millimeter wave frequencies. This is particularly critical in silicon integrated circuits due to the limited transistor gain, efficiency, and breakdown on the active side and lower quality factor of the passive components due to ohmic and substrate losses.
Efficient power combining is particularly useful in silicon where a large number of smaller power sources and/or amplifiers can generate large output power levels reliably. This would be most beneficial if the power combining function is merged with impedance transformation that will allow individual transistors to drive more current at lower voltage swings to avoid breakdown issues [21]. Most of the traditional power combining methods use either resonant circuits and are hence narrowband or employ broadband, yet lossy, resistive networks.
The concept of a solitary wave was introduced to science by John Scott Russell 170 years ago [1]. In 1834 he observed a wave which was formed when a rapidly drawn boat came to a sudden stop in narrow channel. According to his diary, this wave continued “at great velocity, assuming the form of a large solitary elevation, a well-defined heap of water that continued its course along the channel apparently without change of form or diminution of speed”. These solitary waves, now called ‘solitons’, have become important subjects of research in diverse fields of physics and engineering. There is a considerable body of work on solitons in applied mathematics (e.g., [2, 3]), applied physics—especially in optics (e.g. [4-7])—and few works in electronics [8]. The ability of solitons to propagate with small dispersion can be used as an effective means to transmit data, modulated as short pulses over long distances; one example of this is the ultra wideband impulse radio that has recently gained popularity [16].
An important related application is pulse sharpening for the more traditional non-return-to-zero (NRZ) data transmission in digital circuits by improving the edges of the pulses. Improving the transitions by shrinking the rise and fall times of pulses can be useful in other applications, such as high-speed sampling and timing systems. Non-linear transmission lines' (NLTLs) sharpening of either the rising or falling edge of a pulse has been demonstrated on a GaAs technology [9], [10]. However, to the best of applicants' knowledge, to this date there has been no demonstration of simultaneous reduction of both rise and fall times in an NLTL. Neither are the applicants aware of any demonstration of such NLTLs in silicon-based CMOS process technologies.